HP-45 Owner's Handbook 1973 Color

7/29/2019 HP-45 Owner's Handbook 1973 Color

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Hewlett-Packard's interest in computation evolved as a naturalextension of our traditional involvement in measurement problemsolving. At an early date, HP recognized the growing need for afamily of computational products designed to work easily andeffectively with scientific instruments.In 1966 we introduced the first digital minicomputer specificallydesigned to meet this need. Soon after, we followed up with ourfirst programmable calculator. From these beginnings, HP hasnow become an acknowledged leader in the field of computationalproblem solving. More than 20 ,000 HP programmable calculatorsand digital computers are at work in a wide range of applicationsin science, industry, education, medicine, and business. Their effectiveness is further enhanced by a complete line of accessorydevices, ranging from digital tape and disc drives to card and tapereaders, printers, and plotters.Lately we've coupled our experience in scientific problem solvingand computational technology to bring you new dimensions inpersonal computation-the HP-80 Business Pocket Calculator forsolving problems in business and finance, the HP-35 ScientificPocket Calculator for engineering/ scientific applications, and nowthe HP-45 Advanced Scientific Pocket Calculator whose expandedfunctional capability and multiple storage registers allow complexproblems to be handled with unprecedented ease.


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Attention Please!To give you more computing power, your HP-45 works in a consistent and natural way that may be slightly different from previouscalculators you have operated . Even though your new HP-45 issimple to operate, and you can start solving problems immediatelyby following the Quick Reference Guide accompanying the HP-45 ,you will find it worthwhile to read this handbook.


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Table of ContentsHP-45 Owner's Handbook

Introduction . . . . . . . . . . . .. . . . .. . . .. . . .

General Operating InstructionsFundamental Operations

Gettin g Started .Ke yboa rdKeying in and Entering NumbersPerfo rmi ng Simple Arith metic ..Correcting In put Erro rs.Clearing . . . . . . . . . . . . . .Using Disp lay and Round in g Options.Keyi ng in Negative Numbers . . . . . . . . . . . . . . . . .Key ing in Exponents .Perfo rming Sim ple Functions.Find ing Reciproca ls

Finding Square RootsSquaring NumbersRaising Numbers to Powers . .. . . . . . . . ..Using PiUs ing Factoria lsCalcu lat ing Percentage Proble ms.

7

999

111112131314151616161616181820

Operational Stack. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Stack Registers . . . . . . . . . . . 21Manipulating the Stack. 23Performing Combined Arithmetic Processes . 24Serial Calcu lation ........... . . 24Ch ained Ca lculat ion .. . . . . . . . . 24Mixed Chained Calculat ion 25

Last x Register . . . . . . .. . . . .. . .. . . . . . .. .. . . .. . .. .

Data Storage RegistersUnrestricted StorageRegisters R, - R . . . . . . . . . . . . . .. . . . . . . . . . . ..Restricted Storage . .. . . . . .. . .Registers R, - R,Register R . . . . . . .. . . . . . . . . . . . . . . . .Storing and Recalling Data ... .. . .. .. . .. . . . . . . . .

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26262626262627


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Metric/U .S. Unit Conversion Constants .Logarithmic and Exponential FunctionsStatistical Functions .Trigonometric Functions . . . . . . . . . . . . . .Angular Modes. . . . . . . . . . . .. .Degrees-Minutes-Seconds Conversion.Polar/Rectangular Coordinate Conversion .Operating Limits .Accuracy .Underflow and Overfl ow Displ ay Formats.Improper Operations. . . . . . . . . . . . . . . . . . .

Appendixes :

31

32

34373738

39

42424344

Stack Algorithm and Flowchart. 45Hardware Specifications . . . . . . . . . . . . 47

Temperature Range 47Battery Operation . . . . . . . . . . . . . . . . . . 47Recharg ing and AC Line Operati on . 47Battery Pack Replacement. 48

Accessories . 51Calculation Equations . 52Service and Warranty . 53Servici ng .. . . .. . . . .. . .. .. 53Low Powe r . . . . . . . . . . . . . . . . 53Blank Display . . . . . . . . . . . . . . . 53

Warranty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53In War ra nty 53Out of Warranty . . . . . 53Shipping In struct ions . . . . . . . . . . . . . . . . . . . 54Subject Index . . . . . . . . . . 55Keyboard Summary and Index . 58


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IntroductionLittle is understood about the methods used by calculating prodigies to perform their awesome feats. The method used by 10-yearold Truman Henry Safford in 1846 to calculate 365365365365365365' (as described by the Rev. H. W Adams) shows that difficult problems are difficult even for prodigies-" . '. he flew aroundthe room like a top, pulled his pantaloons over the tops of hisboots, bit his hands, rolled his eyes in their sockets, sometimessmiling and talking and then seeming to be in an agony, until, innot more than one minute said he, 733,491,850,208,566,925,016 ,658 ,299,941 ,583 ,225!"Although your HP-45 might not be as much fun to watch, it makescalculating faster and less arduous, because the operational stackand the reverse "Polish" notation used in the HP-45 provide themost efficient way known to computer science for evaluatingmathematical expressions.The HP-45 has far more computing power than previous pocketcalculators. Its accuracy exceeds the precision to which most ofthe physical constants of the universe are known. It will handlenumbers as small as 10-on , as large as 10"" , automatically placesthe decimal point, and allows 20 different options for rounding thedisplay to provide greater flexibility and convenience in interpreting results. The HP-45 provides you with transcendental functions, such as logarithms, sines and cosines; polar/ rectangularcoordinate conversions for handling complex arithmetic, vectors;selective operating modes; and multiple storage registers. Additionally, constants for 'iT and e are provided- as well as threemetric/U.S. unit constants for conversions between centimeters/inches, kilograms/ pounds, and liters/ gallons. Furthermore, statistical capabilities for calculating the mean (arithmetic average)and standard deviation are incorporated in the HP-45.


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To give you an idea of the scope and power of your HP-45, let's convert rectangular x, y coordinates (3 , 4) to polar form (magnitude andangle). To solve, simply enter the known values as follows:Key in 4 (y-coordinate) and press ENTER t , then key in 3 (x-coordinate) and press III to polar) to display the magnitude: 5.00.Press x:y to display the angle: 53.13.I f you want to see the angle with 8 decimal places, press III , henkey in 8 and see displayed: 53 .13010235.To obtain the magnitude, press x:y and see displayed: 5.00000000.Now press 1112 to get back to 2 decimal places in the display.Note that the result is accurate to 9 significant digits. Now compare that with the slide rule solution (accurate to 3 significantdigits) .

Slide Rule Method HP-45 MethodMagnitude = ~ Key in:Angle = tan -' (y/x) 4 ENTER t 3where: x = 3 Display magnitude:y= 4 I I I - -alculate magnitude: x' = 3 x 3 = 9y ' = 4 x 4=16 Display angle:x' + y' = 9 + 16 = 25 x:y__-Vx'+Y' = -f25 = 5.0Calculate angle: tan- ' (y/x) = tan- ' (4/3) =tan- ' (1 .3) = 53.1

Incidentally, no calculator available today (including ours) can handlethe problem given to our child prodigy. Isn't it comforting to know thatpeople can still do things machines can't?


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Fundamental OperationsGetting StartedYour HP-45 is shipped fully assembled with its battery pack in placeand is ready to operate. Slide the power switch to ON. I f anything otherthan 0.00 appears on the display, see Service, page 53 .The display blinks when an improper operation is made. The blinking will stop as soon as CLX is pressed and you may enter a new problem.KeyboardFigure 1 illustrates the keyboard layout. Almost every key performstwo distinct functions. The symbol for th e primary function appearson the key, and the symbol for the alternate function appears above

{Xthe key like this I I .To use the primary function, merely press the selected key; to use thealternate function, press the gold key . Cupper righthand corner) be-

{Xfore pressing the associated key like this . 11. Alternate functionsare indicated like this . [ ~ J t h r o u g h o u t your Handbook.A summary of all keys and an index to where they are used are provided at the back of your Handbook.


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Display

Off-On S W i t C h _ ! - I = = = = = = = = = = " ' " = ~ 1) 'x log 10' SCI Gold Shift Key:III .. iii 0 IT ~ SIN - 1 cos - 1 TAN - 1.. m Ell Ell IIIn' i ,s -+ D_MS D.MS .... tJ.%Control Keys: ~ ~ ~ ~ II

E l B ~ ~~ G E l 1 DEG RAD GRD CLEAR. ENTER t il ] ~ ]

em / in kg / lb Itr / galArithmeti cKeys: G CD i. JUI [ ]JGEi CB [ I ] ~ []JJEi 0 IT ] I . ~ CD

LAST X TT ,.G (I j] ~ IE

Figure 1. Keyboard Layout


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Keying In and Entering NumbersEach time a number key is pressed, that number appears left-justifiedon the display in the order as pressed. Note that a decimal point symbol is included with the number entry keys; it must be keyed in if it ispart of the number. For example, 314.32 would be keyed as 0 CDo 8 0 0 To signal that the number string keyed in is complete, press ENTER t . Now you may key in another number string.I f you make a mistake when keying in a number, clear the entire number string by pressing CLX Then key in the correct number.

Performing Simple ArithmeticIn the HP-45, arithmetic answers appear on the display immediatelyafter press ing an arithmetic key: + , - , x , """ . In an adding machine, the + key adds whatever is already in the machine to the lastentry, and the - key subtracts this last entry. The HP-45 not oniyadds and -subtracts the same way as the old famili ar adding machine,it also mUltiplies and divides this way too-the X key multiplies whatever is already in the machine by the last entry, and the """ key dividesby the last entry. For example, add 12 and 3.

Press: See displayed:3 + - - - - - l . _

Did you notice that you calculated this sum in the same order in whichyou would ordinarily do it with pencil and paper? That's right-youkeyed in 12, terminated the number string and loaded the number bypressing ENTER t . Then you pressed 3 followed by + to get the answer.

This same principle is used for calculating any arithmetic problemhaving two numbers and one arithmetic operator. For example, subtract 3 from 12.Press:

3 -See displayed:

- - - - ~ . -1


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To multiply 12 by 3,Press: See displayed:----...-

o divide 12 by 3,Press: See displayed:----..-Correcting Input ErrorsThe HP-45 automatically stores the last number displayed (last inputargument) that precedes the last function performed. For example, if

you wanted to verify the last input argument from the example above,Press: See displayed: i : A ~ ~ ~ i - - - - - - - - - - I " ~ _ last input argument'- _ _ _ _ J

A special storage register-Last x- is provided for this purpose. Aseach new function is keyed (executed) , the contents of Last x are overwritten with the new value.r - - - - 'L : - ' : ~ : J is a very useful feature for correcting errors , such as pressingthe wrong arithmetic operator key or entering the wrong number. Forexample, if you were performing a long calculation where you meant tosubtract 3 from 12 and divided instead, you could compensate as follows:

Press:3

See displayed:

- - - ~ . ~ - oops-you wantedto subtract- - - - - - - I . ~ _ retrieves last numberdisplayed precedingoperation (division)

X - - - - - - - - - - - - . ~ _ reverses divisionoperation; you'reback where you started i ~ A - ; ; ~ ~ i - - - - - - - - _ I . _ retrieves last number

l..____ J displayed before oper-ation (multiplication)

- - - - - - - - - - - - - I . ~ _ correct operation produces desired results


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r - - - - 'I f you want to correct a number in a long calculation, L ' : . . " : ~ : J can saveyou from starting over. For example, divide 12 by 2.157 after you havedivided by 3.157 in error.

Press: See displayed:3.157 ..- you wanted to divideby 2.157 not3.157 i ~ ~ ~ ~ iL ____ J ..- retrieves last numberdisplayed precedingoperation

X ..- you're back at thebeginning2.157 ..- Eureka!ClearingTo clear the display, press CLX . To clear the entire calculator (except! _ ~ e , r t a i n data storage registers-more about that later), press .L : : ' : . ~ ~ J (Notice that it isn't necessa ry - although it may be comfortingto clear the calculator when starting a new calculation.) To clear everything, including all data storage reg isters, turn the HP-45 off then on.

Using Display And Rounding Optionsup to 15 characters can be displayed: mantissa sign,10-digit mantissa,decimal point, exponent sign, and 2-digit exponent.Two display modes (fixed decimal and scientific notation) and a varietyof rounding options are provided. Rounding options affect the displayonly; the HP-45 always maintains full accuracy internally.Fixed decimal notation is specified by press ing III followed by theappropriate number key to specify the number of decimal places (0-9)to which the di splay is to be rounded. The display is left-justified andincludes trailing zeros within the setting specified. Wh en the calculatoris turned on it "defaults" to III 2; that is, the mode and decimal placese ttings revert to predes ignated ones (III 2) automatically.

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For example,Press : See displayed:123.456-------------; .11141111111 0

Scientific notation is useful when you are working with ve ry large orvery small numbers. I t is specified by pressing [ ~ ~ J ' fo llowed bythe appropriate number key to specify the number of decimal places(0-9) to be displayed. Again, the display is left-justified and includestrailing zeros. For example,

Press: See displayed: r--,L:'':J 6 - - - - - - - - - - - - - . . . ; . ~ r;;l 3 - - - - - - - - - - - - - ~_ _ .J

Now return to 2 decimal places in fixed decimal notation.Press: See displayed:1112---------- . _

Keying In Negative NumbersTo enter a negative number, key in the number, then press CHS (changesign key). The number, preceded by a minus (- ) sign, will appear onthe display. For example,

Press: See displayed:

To change the sign of a negative or positive number on the display,press CHS . For example, to change the sign of - 35.00 now in thedisplay,

Press: See displayed:C H S - - - - - - - - - - - - - - - - - ~ . ~ I11III


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Keying In ExponentsYou can key in numbers having exponents by pressing EEX (Enter Exponent). For example, key in 15.6 trillion (15.6 X 1012 ) , and multiplyit by 25.


..

You can save time when keying in exact powers of ten by pressing EEXand then press ing the desired power of ten. For example, key inmillion (10") and divide by 52.


..

To see your answer in scientific notation with 6 decimal places,Press: See displayed: r--,L ~ ' : J 6 - - - - - - - - - - - - - - ..

To key in negative exponents, key in the number, press EEX , press CHSto make the ex ponent negative, then key in the power of ten. For example, key in Planck's constant (h)-roughly, 6.625 X 10-27 erg. sec.- and multiply it by 50.

Press: See displayed:6.625 EEx l------------. .27 ..

..

..

I f you return to a 1112 se tting, the result is rounded to zero. For example,

Press: See displayed:1112--------------------- . . .


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Performing Simple FunctionsFinding ReciprocalsTo calculate reciprocals of a displayed number, key in the number,then press III. For example, find the reciprocal of 25.

Press: See displayed:25111 _You can also calculate the reciprocal of a value in a previous calculationwithout reentering the number. For example, calculate _ ___lh + Y6 '

Press: See displayed:3111 .. - reciprocal of 36111 - reciprocal of 6+ .. - sum of reciprocalsIII - reciprocal of sumFinding Square Roots

To calculate the square root of any displayed value, press . [ ~ J .For example, find the square root of 16.Press: See displayed:16 . [ ~ J - - - - - - - - - - - - - - - .. -

Now find the square root of the result.Press: See displayed: rFx-1 .. _L __ J - - - - - - - - - - - - - - ~ ~

Squaring NumbersI I ermits you to square numbers with a single keystroke. For example, what is the square of the result in the previous example?

Press:

I ISee displayed:

- - - - - - - - - - - - - - - - - - - - - - ~ . II1II 2squaredRaising Numbers to Powersr - - ,L ~ ~ J permits you to raise a positive number (both integers and deci-mals) to any power. For example, calculate 2" (2 X 2 X 2 X 2 X 2 X2 X 2 X 2 X 2) .

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Press: See displayed:2 ENTER t 9 . r ~ ~ l - - - - - - - - - __ J

Check different decimal settings. 6---- - - - - - - -... 7------------------ . r--,Because a logarithmic routine is used internally to compute ! : ~ J ' theresults may not be accurate to the last decimal place-as illustratedin the example above (see A ccuracy, page 42).Now change the decimal setting back to 2 places and find 8 1.2567 .

Press: See displayed:-----------..-- l1 l i--------------. . . II1IIr--,In conjunction withII L ~ : J provides a simple way to extract roots.

For example, find the cube root of 5.Press: See displayed:---------------..-. ...

--------------i... _ reciprocal of 3 [ ~ ~ J - _ cube root of 5Sample Case: Assume that a body moves along a straight line according to the equation S =-t t' - 4t. Determine its velocity (V =t5 - 4)and acceleration (A = 15 t') at t = 2 seconds, w h ~ r eSolution:

Press:2

V= 3 25 - 4A= 15 .2 4

See displayed: r--,5 L!::J --------.- 1- - - - - - - - - - - - - - - - . . . - l1 l i42

_ velocity4~ ~ l - - - - - - _ ... _L __ J------------- . ._ _ acceleration


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Using 7T" is one of the fixed constants provided in the HP-45 . Merely press [ ~ ~ J whenever you need it in a calculation before executing theapplicable operation. For example, calculate 3".

Press: See displayed:- - - - - - - - - - - - ~ . l1li

Sample Case 1: Find the area A of a circle with a 3-foot radius r,where

Solution :A= " r 2r= 3

Press: See displayed: r--,L _ ~ J - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ I11III311 I11IIIx ---------------1.. _ sq. ft.

Sample Case 2: Find the increas e in the volume of a spherical balloonwhen its radius is increased from 2 to 3 inches. Volume of a sphere isequal to 4/ 3 d 3 Therefo re, 4/3 ".(3)" minus 4/ 3 ,,(2)3 is the increasein volume. The equation can be written

Solution:Press:

1" ((3)3 - (2)3)See displayed:

3 r ~ ; l - - - - - - - - - - - - - - _ I _L__ .J3 . r ~ ; 1 _L__ J---------------------..-- - - - - - - - - - - - - - - - - ~ l1 l i- - - - - - - - - - - - - - - - - - ~ l1 l i

r-,,-l -------------------------I.. l1 l iL__ JX ------------------------------..... l1 l i cubic inchesUsing FactorialsThe r ~ l function permits you to handle combinations and perm utaL__ Jtions with ease. To calculate the factorial of a displayed number merely


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r--,press L . : ' ~ JPress:For example, find the factorial of 5.

See displayed: r--,5 L . : ' ~ J - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ _ 5!Factorials can be calculated for positive integers from hrough 69.Attempting to calculate the factorial of a fractional or negative valueis an improper operation and will result in a blinking display.Sample Case 1, Permutations: How many different ways maya coachassign players, from a squad of 12, to the 9 positions on a baseballlineup? The equation for permutations of 12 things taken 9 at a time is

12!P(l2 , 9) = (l2-9 )!Solution:

Press: r--,12 L ~ ~ J - - - - - - ~

r ~ A ~ ~ ~ l - - - - - - ...._ _ _ _ J9 - 1------1 .. r-- '____I nJ IL__ J

See displayed:12!value is retrievedfrom previous operation

3!number of differ-ent lineups possible

Sample Case 2, Combinations: Let a fair die be tossed ten times. Whatis the probability that you will obtain the number 3 exactly 4 times inthe 10 tosses? The required probability is given by the binomial law

whereSolution:

Press:

C 14 (1 / 6) ' (5 / 6) ' = C 140 5' / 6'0C 14 = 10! / 4! 6!See displayed:

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5'6 ' 0displayed valuerounded to zerovalue extended to4 decimal places


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1112 10 . r ~ ~ l 10!__ Jx r--,4 I n' IL__ J I I 4! r--,6 I n' IL__ J 6! probability

Calculating Percentage ProblemsThe HP-45 simplifies the calculation of percentage problems becauseyou don't have to convert percents to their decimal equivalents beforeusing them; just press the II key after keying in the percent value.Three types of percentage problems are handled:

Finding percentage of number (base X rate) Finding net amount (base + or - percentage) Finding percent difference between a number and a base

( number - base).baseThe equations used for percentage problems are included in Appendix0, Calculation Equations.Finding Percentage: To find the percentage of a number, key in thebase number and press ENTER t . Then key in the percent and pressII.For example, to find 14% of 300, See displayed:- - - - - - - - ... _ percentageFinding Net Amount: An additional feature is that after finding thepercentage, the HP-45 still contains the original base number fromwhich you may calculate the net amount by simply pressing + or - ,respectively. For example,

Press: See displayed:1411----t.. _ percentage

----------__.. . _ net amount (base pluspercentage)


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orPress: See displayed:

1411----l . _ percentage-----------l. _ net amount (base less

percentage)Finding Percent Difference Between Two Numbers: To find the percentdifference between a number and the base, enter the base number andpress ENTER t . Enter the second number, press r : ~ . l . F o r example,L__ Jif you want to find the rate of increase of your current mortgage payment ($240jmo) ove r what you were paying in rent 15 years ago($70 j mo) ,

Press: See displayed:240 r-:..;:l--------1. _ % increaseL___ J

Operational StackStack RegistersThe HP-45 uses the most efficient way known to computer science forevaluating mathematical ex pressions : th e operational stack and reverse "Polish" (Lukasiewicz) notation.The four temporary memory locations (number registers)-arrangedin the form of a vertical stack-are caJ1ed X (bottom register) , Y, Z, andT (top register) , respectively.

Contents Register Namet Tz Zy YX X

NOTE: The contents of the Xregister are always displayed.

To avoid confusion betweenthe name of a register and itscontents, the register is designated by a capital letter andthe contents by a small letter.Thus, X, y, z and I are the contents of X, Y, Z and T, respectively.

When you key in a number, it goes into the X-register- the bottomregister and the only one displayed. When you press ENTER t , this number is duplicated into the Y register. At the same time, Y is moved up toZ and z is moved up to T like this:


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Press: Contents I Register

ENTER t

~ ( c o n t e n t s lost)t / ______ T

Z ~ Z~ ~ ~When you press + , x is added to y, and the entire stack drops to dis-play the answer in X. The same thing happens for - , X and + .Whenever th e stack drops, t is duplicated from T into Z, and z drops toY, as follows :

Press: Contents Register

z-- - - - - -

Look at the contents of the stack as we calculate (3 X 4) + (5 X 6).Directly above the keys pressed you see the information in X, Y, Z and Tafter th e keystroke.

- r u - ~


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Manipulating The StackThe R+ key "rolls down" the stack and lets you review th e contents(in last in-first out order) without losing data. It is also used to repositiondata within the stack. Here is what happens each time you press R+ :

Press Contents IRegister';ttzR+ y YX X

the contents of the stack press R+ four times. The fourth R+ returnsthe stack to its original position (x = 4, Y= 3, z = 2, and t = 1). Note:the stack is raised and t is lost when a keyboard entry or R C ~ operationfollows R+ , unless that entry follows CLX , or ~ .The x:y key exchanges x and y as shown below.

Press Contents [ RegisterI_TZ-zx:y y:=:x::: yX X

) ' . ? ~ , will often find that x and y should be exchanged beforeL ! ! ~ J operatIons.Example: Fi.n_d_2'-,-_ _ ~ _ _ ~ _ _ _ _ _ _ _ _ ~

Press See Remarks9.9.002. x and yare in wrong order.9.00 x and yare in right order

i ~ ~ l 512.00L__ J


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Performing Combined Arithmetic ProcessesThe HP-45 performs combined arithmetic operations-serial , mixedand chained calculations-with ease. Since you now know how theoperational stack works, you can apply that knowledge to the followingexamples.Serial CalculationAny time a new number is entered after any calculation, the HP-45 performs an automatic ENTER t on the result of the calculation. This featurepermits a serial calculation having intermediate results to which a seriesof new values can be applied without your having to write down orstore any of the intermediate results. For example, find the sum of4, 6,8 and 10.

Press: See displayed:4 "- ~ --he same principle applies to serial multiplication, division and subtraction too. Note that an equals key (= ) is not needed since resultsare displayed when a function key is pressed.Chained Calculation

Chained calculations can be used to find the sums of products (addingthe results of two or more multiplication operations) or the productof sums (multiplying the results of two or more addition operations).For example, if you sold 12 items at $1.58 each, 8 items at $2.67 eachand 16 items at $0.54 each, the total sale price is

Press:(12 X 1.58) + (8 X 2.67) + (16 X 0.54)

See displayed:~ - - - - - ~ $-- - - - - ~ $_-------- . . . . $ -~ $1- - - - - - - - - - - - - - - - - - -_" $ total sale price


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Mixed Chained CalculationChained calculations can use any arithmetic operator-divide and subtract as well as multiply and divide . Additionally, a problem may becalculated with any combination of arithmetic operators in both nestedand linked operations. For example, to calculate[ { (12 X 5) - 2 }+ { (8 --:-- 2) + 10 } 1X (213 .08 X 5 --:-- 1.33) --:-- 2Press: See displayed:

You may find the flow chart in Appendix A interesting. I t describes aprocedure (an algorithm) that will allow you to evaluate any expressionon a calculator, such as your HP-45, that uses an operational stack andreverse Polish notation.


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Last x RegisterThelast input argument of a calculation is automatically stored in theLast x register when a function is executed. This feature provides ahandy error correction device (see page 12 for examples)-as well as afacility for reusing the same argument in multiple calculations-sincer----'it allows recall of the argument by pressing L ' : . A . : ' ~ : J The registeris cleared only when the calculator is turned off or when a new argument replaces (or overwrites) the previous one.

Data Storage RegistersIn addition to the operational stack and Last x register, the HP-45provides 9 registers for user storage.Unrestricted StorageRegisters R, - R.Registers R , - R.. can be used for temporary storage without restriction .Values stored in these registers are not affected by calculations or byclearing operations. New values are entered by writing over the old contents; that is , by storing a new number. The contents are lost, however,when the HP-45 is turned off.Restricted StorageRegisters Rs - R,Registers R , - Rs are used internally when performing summationsusing ~ and [ ~ When summations are not being performed,these registers may be used for general purpose storage. However, sinceregisters R, - Rs are not overwritten by new values, they must becleared of existing values by pressing [ ~ ~ ~ ~ J before they are usedin summations.Register R,Register R, is required internally when performing trigonometric functions and polar/rectangular conversions; any values stored there will belost. Otherwise, register R, may be used for general purpose storagein the same manner as registers R , - R..


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Storing And Recalling DataTo store a value appearing on the display (whether the result of a calculation or a keyboard entry), press STO , then press the number key ( ~- ~ ) specifying the storage register. To retrieve the value press ACL ,then press the applicable number key. A copy of the recalled valueappears on the display (X-register); the original value remains in thespecified constant storage register. The number previously on the display is loaded into the V-register unless the keystroke immediately preceding ACe was ENTEA t , CLX or ~ (these keys do not cause the stackto be pushed up by the next data entry ). For example, add 8, 20, 17,43; store the result in R , ; and divide the individual numbers by thestored sum to find what part each is of the total.

Press: See displayed:_ total-- - - - - - - - - - l I _ ~ _ or 9 % of totall- - - - - - - - - _ or 23 % of total_ or 19% of total_ or 49% of total

Performing Register ArithmeticArithmetic operations (+ , - , X, -7-) can be performed between adata storage register and the X-register (display). To modify the contents of the storage register, press STO followed by the applicable operator key ( + , - , X , + ), then the number key specifying thestorage register. For example, store 6 in register Rl then incrementitby 2.

Press: See displayed:------- _ 6 ---7 R,-----. . . . _ r , + 2 ---7 R,To see what is now stored in Register R "

Press: See displayed:AC ~ , - - - - - - - - - - 1 ~ _ r, ---7 X (display)

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Now subtract 3 from the contents of R, (8).Press: See displayed:

- - - - - - - l . ~ _ r , - 3 - 4 R,--------- ; . _ r, ---'> X (display)Conversely, to alter the X-Register (displayed value) without affectingthe contents of the data storage register or the other stack registers,

press RCL , the applicable operator, then the number key specifying thestorage register. For example, add the current value stored in R, (5.00)to a new entry (2).

Press: See displayed:------l..... 2 + r, - 4 X (display)R C ~ IT] _ r, - 4 X (display)

Subtract the contents of register R , (5.00) from a new entry (11) .Press: See displayed:- - - - . ~ . . 11 - r, - 4 X (display)

- - - - - - - - -.... , ---'> X (display)Now combine several operations.IT] .. _ 3 ---,> R.

- - - - - . ~ _ I , + 2 - 4 R,------; . _ r , -7- .25 - 4 R,--------- . _ r, ---'> X (display)

- - - - - . ~ _ 5 X r, - 4 X (display)To use a data storage register as a counter or tally register, you must setthat register to zero-either by clearing or by storing O. To incrementthe counter use aexample :

Press: See displayed:o STO 0 - .. - 4 R,; sets counter to 00- __ . + 1 - 4 R 4 ; increments counter


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0- _ r4 + 1 - 7 R. ; increments counter0-- r, + 1 -7 R,; increments counter0-_ , - 1 -7 R,; decrements counter- - - - - - l . . _ L, -7 X (display); current value

of counter displayedSample Case: Hardhat Construction Company must file a quarterlyreport showing payroll information. Produce a report sorting the rawdata (hours worked) according to four applicable rates : # 1 = $6.735 /hr. for straight time, # 2 = $10.1025/ hr. for 1.5 time, # 3 = $13.47/hr. for double time, # 4 = $1.75/ hr. for showup-no work time. Calculate the hours and gross payroll by rate and craft ; use the data fromthe abbreviated time card in Figure 2.

Hardhat Construction, Inc.Time Card Summary - Craft No.7Date: July 3,1973

Name Hours Rate No.Pete r Dickinson 2 11 21 4France Rode S 12 23 3Arlin Laymon 8 14 31 4

Figure 2. Time Card DataSolution:

Press: See displayed:OFF-ON (or store Os in R" R" R3 , R,)6.735 STO ~

Rate Amount(S .735/hr)(10.1025/ hr)(1.75 / hr)

(13.471hr)


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2 OJ - + -] + - OJ + - so rts and stores hours0 - according to app licable2 + rate-keeps running3 ~ + - tally of hours8 OJ - ~ -] - total craft hours - total hours, rate # 1$ total, rate # 1(straight-time pay)RCL 0 - total hours, rate # 2$ total, rate # 2(1.5-time pay)+ $ gross payroll subtotalRCL ~ - total hours, rate # 3$ total , rate # 3 (double-time pay)+ $ gross payroll subtotalRCL 8] - total hours, rate # 4$ total, ra te # 4(show-up pay)+ $ gross payroll forcraft # 7


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Metric/U.S. Unit ConversionConstants!The HP-45 provides built-in conversion constants (accurate to 10 digits)for:

tt Centimeters-to-inches and inches-to-centimeters (1 inch =2.540000000 centimeters) Kilograms-to-pounds and pounds-to-kilograms (1 pound* =0.453592370 kilograms) Liters-to-gallons and ga llons-to-liters ( l gallon* *= 3.785411784liters)

To use these constants, key in the measure to be converted, press . 'then press the desired constant key followed by the applicable operator:X to obtain metric equivalents, """ to obtain U.S. equivalents.

med constant key is pressed or when a user stored constant is recalled.For example,

Press: See displayed:12 r ~ ~ / ; ~ l - - - - - - - - - - - - - ... _-_ _ _ _ J

X - - - - - - - - - - - - - - - - - - - - - - - - - - ~ . _Sample Case 1: I f an 8" x 10" drawing is to be reduced to 85% of itsoriginal size, what is the finished size in terms of centimeters?Solution :

Press: See displayed:8511-------- . . . . , .. _ inches [ ~ ~ ~ ~ J .. _ conversion constant

1-------------- ; .. _ centimeters------I. _ inches

[ ~ ~ ~ ~ J - - - - - - - - - i . . . _ conversion constantx l-------------- ; .. _ centimeters (thet Ref: National Burea uof Standards, 1967

tt Changed in 1957 by internationa l agreement* Avoirdupo issystem... U.S. liquid measure

31

finished size is 17.27cm X 21.59 cm)


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Sample Case 2: I f you needed a baby elephant for any reason (andcould afford to maintain it), how much would shipping costs be in dollars if the baby weighs 500 ki lograms and the shipping cost per poundwere 23?Solution:

Press: See displayed:500 [ ~ ~ ~ ~ J ------'l. .,------------------'l. '".23 X - - - - - - - - -'l. $ . conversion constant, pounds total shipping cost

Sample Case 3: An American in Germany purchases 16 liters of wine.Since the duty is figured on gallons, how many gallons does he have?Solution:

Press: See displayed:16 . [ ~ ~ ~ ~ J - - - - - - - ---. _ conversion constant

.. gallonsSample Case 4: I f you pick up a Mercedes Benz in Germany and themileage is quoted at 7 kilometers per liter, would this car be expensiveto run by U. S. standards?Solution:

Press: See displayed:7~ ; ~ l .. conversion constant. ____ JX .. W, kilometers/gallon r ~ ~ - ~ il ____ J .. II. conversion constant

.. i . cm/ft

.. -Mi cm/mile.. Ai km/mile.. e miles/gallonLogarithmic and Exponential Functions

The HP-45 computes both natural and common logarithms as well astheir inverse functions (antilogarithms):


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IIIII

is log. (natural log) ; takes log of value in X-register to basee(2.718 . . . .is antilog. (natural antilog); raises e (e = 2.718 . . . to thepower of value in X-register. (To display the value of e,press 1 III )

r l o ~ l is log ,o (common log); takes log of value in X-register toL _ _ J base 10 r ~ o - : ; l is antilog lO (common antilog); raises 10 to the power of

L _ _ J value in X-register.Sample Case 1: Suppose you wish to use an ordinary barometer as analtimeter. After measuring the sea level pressure (30 inches of mercury)you climb until the barometer indicates 9.4 inches of mercury. Howhigh are you? Although the exact relationship of pressure and altitudeis a function of many factors , an approximation is given by

. 30 30Altitude (feet) = 25,000 In Pressure = 25,000 In 9.4Solution:

Press: See displayed:...411------

x 1- - - - - - - - - - -"" feet altitude(we suspect you are on Mt. Everest-29,028 feet)

Sample Case 2: The 1906 San Francisco earthquake, with a magnitudeof 8.25 on the Richter Scale is estimated to be 105 times greater thanthe Nicaragua quake of 1972. What would be the magnitude of thelatter on the Richter Scale? The equation is8.25 - (log 105)

Solution:Press: See displayed:

105 -- - - - - - - - - - - - ...... _ rating on Richter Scale33


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Statistical Functionsr - - ,The statistical function ~ ~ J is used to find the mean (arithmetic aver-

age) and standard deviation (measure of dispersion around the mean)of data entered and summed. Options are provided to enable you tointeract with and modify results by adding new data or correcting errors. Also, the number of entries and sum of the squares-as well asthe sum of entries in two dimensions-can be obtained. Summation/l : -averaging calculations also use the ~ (sigma) key to sum the num-

bers used in calculating means and standard deviations. Because the~ function uses storage registers R ,-Rs, these registers must becleared with i ; ' : - E ~ ~ " 1 before pressing ~ or errors could result.L____ JInformation is entered as follows :

CD Press . [ ~ ~ ~ R J to assure that registers R ,-R, are clear of previous data.

Key in each value and sum with ~ key. To correct an incorrectvalue before it is loaded with the keystroke, press CLX . Afterthe value is summed, correct by (a) reentering incorrect value,then (b) pressing . [ ~ ~ J ' followed by (c) entering correctvalue, and finally (d) pressing ~ ; then continue entering values.The last ~ pressed provides the number of entries.

@ Press . r;:"1 to obtain mean.L__ Jo Press x:y to obtain standard deviation.o I f there are more values to be included-say if you want to addto the data sample and modify results-key in and press ~after each.

Additional information is also available by performing steps 6-10(in any order).@ Press R C ~ ~ to obtain number of entries.(]) Press R C ~ [II o obtain sum of squares for X-register entries. Press RCL [2] to obtain sum of X-register entries.@) Press RCI ~ to obtain sum of Y-register entries.*

*A Yregister entry is any value residing in the Yregister at the time ~ is pressed;e.g., if the entry sequence isn, ENTER t n, ~ where: n, = yvaluen, = xvalue

34


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@i Alternatively, press RCL lB to obtain sum of X-register entries,and x:y to obtain sum of V-register entries.

Sample Case 1: In a recent survey to determine the average age of the10 wealthiest people in the U.S., the following data were obtained:62 84 47 58 68 60 62 59 71 73

Of the ages given, what is the mean; the standard deviation?Solution:

Press: See displayed: r C ~ ~ ; R j .. _L_ __ J62 lB 84lB 47 lB 58lB 68lB60 lB 62 lB 59 lB 71 lB 73 lB -r i . ~ l - - - - - - - - - - - - I . ~L__ J -: y - - - - - - - - - - - - - - - I . ~ -

number of entriesmeanstandard deviation

Add two more ages (87 and 49) after the initial calculation . What isthe new mean and standard deviation?Press: See displayed:

87 lB 49 lBl-------- . . _ number of entries r--, _I ' .S I . . new mean.. __ .Jx:y .. _ new standard deviation

Sample Case 2: Perform error recovery after entering the second valuein error.Solution:

Press: See displayed: r c : ~ R l - - - - - - - - - - - - - . , . ~ ____ J62 lB 44lB 4 4 . [ ~ ~ J 8 4 l B47 lB 58lB 68 lB 60 lB 62lB59 lB 71 lB 73 lB------- l . _ number of entries r--, _I X,s I . . meanL__ Jx:y .. _ standard deviation


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Sample Case 3: Find the sum of the ages entered, sum of the squares,and the number of entries as well as the mean and standard deviation.Solution:

Press: See displayed:. ..----,L : ~ ~ ~ J - - - - - - - - - - - - - - - - ~ 6 2 ~ 8 4 ~ 4 7 ~ 5 8 ~ 6 8 ~6 0 ~ 6 2 ~ 5 9 ~ 7 1 ~ 7 3 ~ ~.r--,i , s I __ J0

R C ~ ~ R c ~ 0

number of entriesmeanstandard deviationsum of numbersentered (x-entries)sum of squares(x-entries)number of entries

Sample Case 4: Assuming that every member of the sample over 65 isa female, calculate the mean, standard deviation, and the sum of ages- as well as the total number of females. Enter a I for female and 0for male before keying in each value.Solution:Press: See displayed: i ~ ~ ~ ~ i .. _~ - - - - ~ - - - - - - - - - - - - - - - - - - ~oo

o

6 2 ~ 14 7 ~ 0

6 8 ~ 06 2 ~ 0

8 4 ~

r i ~ l - - - - - - - - - - - - - - - - - - - - ....... __ J x:yJ- - - - - - - - - - - -_. -- number of entriesmeanstandard deviationsum of agesnumber of females


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Trigonometric FunctionsThe following trigonometric functions are provided:

III (sine)r - - - - ' (arc sine)StN- 1 IL ____ J

III (cosine)r - - - - 'I cos- 1 IL____ J (arc cosine)

III (tangent)r - - - - ' (arc tangent)TAN ' IL____ J

To use the III III and III unctions, key in the number and pressthe appropriate function key. To use the arc functions, press . , thenpress the associated function key. For example, find SIN-l (.866).

Press: See displayed:.866 [ ~ I ; = ~ J _ degreesNote that trigonometric functions use storage register 9; any valuestored there will be overwritten during a trigonometric calculation.

Angular ModesTrigonometric functions can be performed in anyone of three angularmodes: decimal degrees, decimal radians and decimal grads-the latterbeing a 100th part of a right angle in the centesimal system of measuring angles. Note that trigonometric functions assume decimal anglesregardless of angular mode. To select a mode, press . ' then pressthe associated key: D ~ ~ i or f ; A ~ l or r G - R ~ lL__ J L__ J L __ JThe mode selected will remain operative until a different mode isselected, or until the calculator is turnf:d off; when turned back on, theHP-45 automatically defaults to decimal degrees mode.Sample Case 1: Find the cosine of 35 0 I f the HP-45 is not already indegrees mode, press [ ~ E ~ J before performing the calculation.Solution:

Press: See displayed:3 5 1 1 1 - - - - - - - - - - - - - - - - - - ~ III


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Sample Case 2: Find the tangent of 6 radians.Solution:

Press: See displayed: r;A-;1 6 .... - - - - - - - - - - - - ~ . ~. __ J IIiIiISample Case 3: Find the arc sine of .5 in grads .Solution:

Press: See displayed: r-- ' r---- 'L ~ . : ' J L : ' ~ _ = ~ J - - - - - - - - - - - -egrees-Minutes-Seconds Conversion

Displayed angles can be converted from any decimal angular mode todegrees-minutes-seconds, in the format dd.mmss, by pressing . ~ ~ D ~ ~ S J .Conversely, to convert an angle displayed in degrees-min utes-secondsto the decimal equivalent in the specified angular mode,press . ~ = M ~ ~ ~ JThis feature is also useful in calculating problems dealing with time(hours-minutes-seconds) too. ---,Note that the result of a L : ~ ~ : : J conversion is rounded to the nearestsecond both internally and on the display . Conversions involving angles

~ 10' degrees are an improper operation.Sample Case 1: Assume a surveyor wants to add 2 angles: 10 0 8' 56"and 2 0 17' 42". These must first be converted to decimal degrees before adding and then converted back to degrees-min utes-seconds.Solution:

Press: See displayed: [ ~ E ~ J 10.0856 [ ~ ~ ~ : J - decimal degrees2.1742 [ ~ ~ ~ : J decimal degrees+ decimal degrees

12 0 26' 38"Sample Case 2: Find the arc sine of .55 in degrees mode and convertto degrees-min utes-seconds.Solution:

Press: See displayed: r--, r---,L':.':'J .55 L ~ ~ _ J - - - - - - - , . . . decimal degrees [ : ~ ~ ~ J - - - - - - - - - - " 33 0 22' 01"


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Sample Case 3: Using the data from Sample Case 2, above, calculatethe arc sine of .55 in radians mode and convert the result to degreesminutes-seconds.Solution:

Press: See displayed: f ; A ~ i .55 . i ~ ~ : - 1 1 _ _ _ _ _ - - 1 " ~L __ ~ ___ J radians i : ~ ~ ~ l - - - - - - - - - - - ..____ J 33 22' 01"Polar/Rectangular CoordinateConversion

Two functions are provided for polar/rectangular coordinate conversion. To convert values in X and V-registers, (representing rectangularx, y coordinates, respectively) to polar r, e coordinates (magnitude andangle, respectively), press III.Conversely, to convert values in X and V-registers representing polar(r, e, respectively) to rectangular coordinates (x, y, respectively) , press

r : ~ lL__ .JBecause polar/rectangular conversions involve trigonometry, storageregister 9 is used. Thus, any values previously stored in this registerwill be overwritten when coordinate conversions are performed.Sample Case 1: Convert rectangular coordinates (4, 3) to polar formwith the angle expressed in degrees.


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Solution:Press: See displayed:

-------l . _ magnitudeJ----------------.. _ angle in degrees

S,Ullple Case 2: Convert polar coordinates (8, 120) to rectangularcoordinates.

y

Solution:Press: See displayed: i;E7,j 120 ENTER t 8 r : ; j _ _ x-coordinateL __ J L __ Jx:y .. _ y-coordinate

By combining the polar/ rectangular function with the accumulationr-function, ~ , you can add and subtract vector components. The sums

of these are contained in storage registers R, and R,:f r == Xl X2 . . . Xn == LXr, = y, Y2 . . . Yn= LY

To display the contents of registers R, and R s , press RCL ~ to obtain th e sum of x-coordin ates (register 7) ; then press x:y to obtain thesum of y-coordinates (register 8).


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Sample Case 3: Sum 2 vectors V" V2 having polar coordinates (8,30), (12, 60), respectively. Represent the sum V in terms of polarcoordinates (r, 0).

Solution:Press: See displayed: r ~ ~ ~ ; l - - - - - - - - - - - - - - - - - - - - - - - - - - ~ _____ J60 ENTER t 12 r:-;'i .. l1liEl L __ . . l1li

8 . r ' : ~ i l1 l i__ J l1 l i- - - - - - - - - - - - - - - - - - ~ . . l1li- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -.. _ magnitude r

x : y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ . l1l i angle 0


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Operating LimitsAccuracy"Accuracy specifications for the HP-45 depend on the operation performed. The elementary operations ( + , - , X , + ,III ' Fx-l ,I I = 0 = - j have a maximum error of 1 count in the 10th ( le-a'stsignificant) digit. Errors in these elementary operations are caused byrounding answers to the 10th (least significant) digit.Percent(. r ~ and factorial i ~ - l functions are accurate to 1L__ J L__ Jcount in the ninth digit. Values converted to degrees-min utes-seconds

[ ~ ~ ~ ~ are rounded to the nearest second.An example of round off error is seen when evaluating (,,(5)2. Rounding VS to 10 significant digits gives 2.236067977 . Squaring this number gives the 19-digit product 4.999999997764872529. Rounding thesquare to 10 digits gives 4.999999998. I f the next larger approximation (2.236067978) is squared, the result is 5.000000002237008484.Rounding this number to 10 significant digits gives 5.000000002.There simply is no lO-digit number whose square is 5.000000000.Accuracy specifications for operations using the mean function [ ~ ~ Jdepend upon the data used and number of entries.The accuracy of the remaining operations (trigonometric, logarithmic and exponential) depends upon the argument. The answer that isdisplayed will be the correct answer for an input argument having avalue that is within N counts (see table below) in the tenth (least significant) digit of the actual input argument. For example, 1.609437912is given as the natural log of 5 when calculated on the HP-45.However, this is an approximation because the result displayed(1.609437912) is actually the natural log of a number between4.999999998 and 5.000000002 which is 2 counts (N = 2 for logarithms) in the 10th (least significant) digit of the actual input argument.

Accuracy statements are given only as a genera l gu ide which , to the best of our know ledge , defines the maximum erro r for the respective functions.


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Values for NOPERATIONr--, . I Ilog I x, X I and .L __ Jtrigonometricr--.,I yx 1L __ J

r - - ,I lOx IL__ J.... r : ~ l... L__ J

VALUE OF N2'3 "

4 for y, and 7 forx

4* Logarithmic operations have an additional limitation of 3 counts in the 10th (leastsignificantl digit in the displayed answer.

** Trigonometric operat ion s have an additional accuracy limitation of I x 10-' in thedisplayed answer.

Underflow and Overflow Display FormatsTo ensure greater accuracy, the HP-45 performs all calculations byusing a ten-digit number and a power of ten. This abbreviated form ofexpressing numbers is called scientific notation; i.e., 23712.45 =2.371245 X 10" in scientific notation.I f a number is too large for th e display format specified, the HP-45automatically displays the number in scientific notation. For example,if you keyed in 100, and pressed III 8, the calculator wi ll display thenumber in scientific notation because there isn't enough room to display 8 digits after the decimal point.

Press: See displayed:l1li8..

Numbers whose magnitude is less than 1, and are too small to be displayed in the specified III ormat, are displayed as zero. For example,the number .000396 is displayed in III 3 format as follows:

43


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Press:1113.000396.,.--'L ~ J 3 111 6 ,.__ ,

See displayed:

When a L ~ ~ J setting is used, values. are displayed rounded to thenumber of decimal places specified. Values having a magnitude of

~ 10, oo are displayed as 9.999999999 99 . Values having a magnitude of < 10-" are displayed as zero.

Improper OperationsI f you attempt a calculation containing an improper operation-saydivision by zero-an error signal is triggered and a blinking displayappears. To clear, press CLX , or any other key that doesn't triggeranother error.The following are examples of improper operations:

, where x = 0r ~ ; l ,where y ~ 0L__ J .....rFx-l ,where x < 0L __ J ,where x = 0

r ~ ~ l ,where x < 0 or is not an integerL __ Jr i , ~ l ,where number of entries is < 2L__ Jr - - - - 'L : ~ ~ : J ' where angle converted:;: 100,000 (:;: 10')

r ~ ; ; ~ : l ,where angJe converted::): 100,000 ( ~ 105)L____ -'[ ~ ~ J ,where x ~ 0 , where x ~ 0

[ ~ ; ~ ~ J 'where\x\is > 1[ ~ ~ ~ ~ J ' where I l is > 1


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Appendix AStack Algorithm and Flow Chart

The flow chart in Figure 3 allows you to evaluate any expression ona calculator using an operational stack and reverse Polish (Lukasiewicz) notation. Although the general solution requires an operationalstack of unlimited length, the four-register stack in your HP-45 is adequate for most practical problems. Before using the algorithm, writeyour expression in serial form. All expressions can be written in serial2form. For example, 3+ 1 / 2) becomes 2/(3 + (l / 2.According to our algorithm, the solution can be obtained for any expression by entering the numbers in the order in which they occur.Use the algorithm to solve (3 + 4) [log (25y7+ 9)+ 6] .

Press See Displayed Flow Chart Reference3 3. A

3.00 04 4. A

7.00 C7.00 0

25 25. A25.00 0

7 7. A7.00 09. A

+ 16.00 C.rrx-j___ J 4.00 BX 100.00 C

. r ' ~ g - i___ J 2.00 B2.00 D6 6. A8.00 C56.00 C

* You may om it these steps because your HP-45 performs an automat ic


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Legend: r--, One number (monadic) operations are things like L ~ J . , etc. You may omit this step if yo u've done any operation on the last numberentered.

Figure 3. Stack Flow Chart

Note that the expression cou ld have been written :(log [ ~ 25J + 6) . (3 + 4). Also, it could have been evalu-ated-us ing the algorithm- in fewer steps:(7 ENTER t 9 + i/il 25 X r l o ~ l 6__ L__ J

X ). Try it.


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Appendix BHardware Specifications

Temperature RangeMode Temperature C

Operating OC to 50CCharging 10C to 40CStorage - 40C to 55C

Battery Operation

Temperature of32F to 122F50F to 104F

- 40F to 131F

Use only the HP Rechargeable Battery Pack, Model 82001A, whichhas been tested and is warranted for one year. The battery providesthree to five hours of continuous operation . By turning off the powerwhen the calculator is not in use, the HP-45 battery power will lasteasily throughout a normal working day .All decimal points light in the display when 2 to 5 minutes of operationtime remain in the battery pack. Even when all decimal points areturned on, the true decimal position is known because an entire digitposition is allocated to it.Example:

l True decimal positionOperating the calculator for more than 2 to 5 minutes after this lowpower indication first occurs may result in calculation errors. The battery pack must be recharged by connecting the HP-45 to its batterycharger eHP Model 82002A).Recharging and AC Line OperationThe HP-45 should be turned off before plugging in the charger. I t canbe turned on again after the charger is plugged into the power outletand can be used during the charging cycle. The HP-45 can be operatedcontinuously from the AC line if desired. There is no danger of overcharging the battery.After 14 hours, a completely discharged battery will be fully charged.Shorter charge periods will allow reduced battery operating time. Forconvenience, overnight charging is recommended.


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CAUTIONTo prevent damage to the calculator, the position of theline voltage select switch on the battery charger mustbe set to the proper line voltage.

1. Turn the HP-45 power switch to OFF.2. Insert battery charger plug into the rear connector of the HP-45

and insert power plug of battery charger into the power outlet. TheHP-45 will not operate when connected to the recharger unless therecharger is connected to a live power outlet.

3. Slide the power switch to ON, see that 0.00 is displayed.4. Slide powe r switch to OFF if you don 't want to use the calculatorwhile it is charging.5. At end of the charging period, you may continue using your HP-45with AC power or proceed to next step for battery operation.6. With the power switch at OFF, disconnect battery charger frompower receptacle and the battery charger from HP-45.Temporary degradation, peculiar to nickel-cadmium batteries, maycause a decrease in the operating period of the battery pack. Shouldthis happen turn the HP-45 on for at least five hours to discharge thebatteries completely. Then put it on charge for at leas t 14 hours. Thisshould correct the temporary degradation.I f the battery pack won't hold a charge, it may be defective . I f thewarranty is in effect, return the pack to Hewlett-Packard accordingto the instructions on page 54. I f the battery pack is out of warranty,use the accessory order card , provided with your HP-45, to order anew battery. Remember, you can use your HP-45 on AC power untilthe replacement battery pack arrives.Battery Pack Replacement1. Turn power switch to OFF and disconnect the battery charger.2. Slide the two battery-door latches (the top feet) toward middle ofcalculator.


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3. Let battery door and battery-pack fall into palm of hand.

5. Insert the battery pack so thatits contacts face the calculatorand contact is made withbattery connectors.

4. See if the battery connectorsprings on the calculator havebeen inadvertently flattenedinward. I f so, bend them outand try the battery again.


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7. Close the battery door by pressing it gently while sliding thetwo battery-door latchesoutward.

6. Insert the bottom of thebattery door behind therefaining groove and closethe door.

NOTE: If you use your HP-45 extensively in field work or duringtravel, you may want to order the Model 82004A Battery Holderand Pack, consisting of battery charging attachment and sparebattery pack. This enables you to charge one pack while usingthe other.

CAUTIONDo not try to burn old batteries. They may EXPLODE!


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Appendix CAccessories

Standard and optional accessories for the HP-45 can be ordered bycompleting and mailing the order card provided. We will send you additional order cards as new optional accessories are added to ourproduct line.

Standard AccessoriesHP-45 Quick Reference GuideBattery PackBattery Charger/AC AdapterDeluxe Travel Safety Case

Soft Carrying CaseHP-45 Owner's HandbookPersonalizing Labels (4 each)Optional Accessories

Battery Holder and PackSecurity CradleHard Leather Field Case

Model/Pari No.00045-9030382001A82002A82014A82012A00045-903007120-2946Model/Part No.82004A82007A82006A


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Appendix DCalculation Equations

The following table shows the data fl ow and equations used in thosecalculations where th e formula is not se lf-evident.

Function Formula.. x y .1 O O ~ x y ~ yr - - - ,

100 . x - y ~ X; Y Yt::."10 IL___ J YII y ; ; - + y . ~ X

t a n L ~ Yxr - - - , X cos y ~ X~ R IL ___ J x sin y y[B + 1 ~ R , ~ X

+ x ' ~ Rr, + x ~ R,r, + y ~ R,r--- .... r, - 1 R , ~ Xr - IL ___ J

r. - x ' ~ R.r, - x ~ R,r, - y ~ R,r---' ~ Xi , s IL ___ J r,

~ _ [r . -!LJ ~ yr, - 1 r,


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ServicingLow Power

Appendix EService and Warranty

All decimal points light to warn you that you have 2 to 5 minutes ofoperating time left. You must then either: Operate from AC power Charge the battery pack Insert a fully charged battery pack

Blank DisplayI f the display blanks out, turn the HP-45 off then on. I f 0.00 does notappear on the display, check the following:

1. If battery charger is attached to HP-45, make sure it isplugged into outlet.2. Examine battery pack to see if it is discharged or is notmaking contact.3. If display is still blank, try operating the HP-45 from the AC line.4. If, after step 3, display is still blank, the HP-45 is defective(see warranty section).

WarrantyIn WarrantyThe HP-45 is warranted against defects in materials and workmanshipfor one year from date of delivery. During the warranty period we willrepair or replace components that prove to be defective, provided theyare returned to Hewlett-Packard according to instructions (see Ship-ping Instructions). No other warranty is expressed or implied. We arenot liable for consequential damage.Out of WarrantyBeyond the one-year wa rranty period, your calculator will be repairedfor a moderate charge. Return the HP-45 along with all standard accessories (see Shipping Instructions) . I f only the battery pack is defective, simply order a replacement on the Order Card provided.


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Shipping InstructionsMalfunctions traced to the calculator or battery charger require thatyou return the following to us:

Your HP-45 with all standard accessories in their travelsafety case A completed Service Card (from back cover pocket of this manual)

I f a battery pack is defective and within- warranty, return the following to us: Only the defective battery pack A completed Service Card (from back cOver pocket of this manual)

Send returned items safely packaged to the address shown on the Service Card.Under normal conditions, your calculator will be repaired and reshipped within two days of receipt at this address. Should other problems or questions arise regarding service, please call the applicableservice telephone number on the Service Card, or call Advanced Products Division, Customer Service, at (408) 996-0100.


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Subject IndexAccessories, 51Accuracy, 42Addition function, 11Angular mode options, 37Antilog functions, 32, 33Arc cosine function , 37Arc sine function, 37Arc tangent function, 37Arithmetic operations: chained, 24; combined, 24; general description o f,11; serial , 24Arithmetic: register, 27; vector, 40Battery: operation of, 47; recharging of, 47; replacement of, 48Battery condition, low, 47Battery pack, 9Calculation equations, 52Centimeters/inches conversion, 31Chained calculation, 24Changing sign, 14, 15Clearing operations: calculator, 13 ; data storage register, 26; display, 13;general description of, 13 ; last x register, 26Combinations, 19Combined arithmetic operations, 24Common antilog function , 33Common log function , 33Constants, preprogrammed: e, 33; metric/ U.S. unit conversion, 31; Pi, 18Controls: data manipulation , 12,23 ; data sto rage register, 27; display,9,13; operational , 9, 13, 14, 15, 22, 24; rounding, 13Conversion constants, 31Conversions: centimeters/ inches, 31; degrees-minutes-seconds, 38;

kilograms/pounds, 31, 32; liters/ gallons, 31, 32; metric/ U.S. units, 31 ;polar/rectangul ar coordinates, 39Correcting input, 12, 26Cosine function , 37Cube root, 17Data: moving and manipulation of, 23; recalling, 27; storing, 27Data storage registers: control of, 27; general description of, 26;restricted, 26; unrestricted, 26Decimal, fixed , 13Decimal place setting, 13Degrees-minutes-seconds conversion, 38Degrees mode, 37Display: blank, 53; blinking, 9, 44; control of , 9, 13Display characters, 13Display formats: overflow, 43; underflow, 43Display modes: fixed decimal, 13; scientific notation , 13


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Display and rounding options, 13Division function , 11Dyadic operations, 46Dynamic range, 7, 44e, use of, 33Entry operations: exponents, 15; negative number, 14; numbers , 11Error: input, 9; rounding, 42Error correction , input, 12Error signal, 44Exchanging contents of x and y, 23Exponent : keying in and entering, 15; negative, 15Exponential functions, 16, 32, 33Factorial function , 18Fixed decimal display, 13Go ld key, 9Grads mode, 37Hardware specifications, 47Input error correction, 12Interactive functions (see Summat ion Function)Keyboard, 9Keying in numbers, 11Ki lograms/ pounds conversion , 31, 32Last x register, recalling, 12, 26Liters/U .S. gallons conversion, 31, 32Logarithmic functions, 32, 33Malfunctions, 53Mean function, 34Metric/ U.S. unit convers ion constants, 31Mixed chained calculation , 25Mode: angular, 37; degrees, 37; grads, 37; radians, 37Monadic operations, 46Multiplication function , 11N atural antilog functions, 33Natural log function, 33Negative exponent, 15Negative numbers, keying in, 14Numbers: keying and entry of, 11; negative, 14; powers of, 16Operation improper, 9, 44Operational controls, 9, 13, 14, 15,22,24Operational stack: algorithm and flow chart of, 45 ; general description of, 21Operating limits, 42Overflow display format, 43


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Percentage functions, 20Permutations, 19Pi (7T), 18Polar/ rectangular coordinates conversion, 39Power switch, 9Powers of numbers, 16Radians mode, 37Range: dynamic, 7, 44; temperature, 47Recalling data, 27Recalling Last x, 12Reciprocal function, 16Register arithmetic: general description of, 27; use of, as counter, 28; useof, in recall operations, 28; use of, in store operations, 27Registers: data storage, 26; Last x, 12,26; working storage , 21Roll down stack, 23Rounding, 13Rounding error , 42Scientific notation, 13, 14, 43Serial calculation, 24Service, 53Shipping instructions, 54Sign, changing of, 14, 15Sine function, 37Square root function, 16Squaring function, 16Stack: algorithm and flow chart of, 45; manipulation of, 23; operation of,21; roll down of, 23Standard deviation function , 34Statistical functions, 34Storage registers: clearing of, 26; data , 26; restrictions on, 26;working, 21, 23Storing data, 27Subtraction function, 11Summation function: decrement using, 34; error correction in, 34; generaldescription of, 34; increment using, 34; two dimensional, 34, 40;use of, in polar/ rectangular coordinates conversion , 40Tangent function, 37Temperature range specifications, 47Trigonometric angular mode options , 37Trigonometric functions, 37Underflow display format, 43Vector arithmetic , 40Working storage registers , 21, 23Warranty, 53


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Keyboard Summary and IndexKEY FUNCTION jOPERATION Page

OFF " ON Power switch . . . . . . . . ........... . . . . . . . . . . . . . . 9r- - '

L ~ ~ J Exponential .r - - ,I log IL__ J

Reciprocal . . .Common logarithm

16,1716,17

33

Natural logarithm . . . . . . . . . . . . . . . . . . . . . . . . . 33r--,I 10 X IL__ J Common antilogarithm ............ . . . . . . . . . . . . 33I I Natural antilogarithm . . . .......... . . . . . . . . . . . . 33r - - ,

L ~ ' : J Scientific notation display mode. . . . . . . . . . . . . . . 14,43III

Fixed decimal notation display mode . . . . . . . . . . . 13 , 439old key; alternate function

riii Square root of x .1..__ .J . . . . . . . . . . . . . . . . . 16II x squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16r : ~ l Polar-to-rectangular conversionL__ JII Rectangular-to-polar conversion

f S ~ ~ - - 1 1 Arc sineL___ JIII Sine . .

i c ~ ; - Arc cosin eL___ J13 Cosine . .r T : ~ - ' l Arc tangentL___ JIII Tangentr - - ,L ~ ~ J Factorial.x:y Exchange x and y . .

r ; , ~ l Mean, standard deviationL__ JR+ Roll down stack . . .

. . . . . . . . . . . . 393937

. ....... 37373737

. . . . . . . . . . . . . . . 37. .......... 18

23 , 34, 4034

. . . . . . . . . . . . . . 23


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i : ~ ~ ~ l Convert 10 degrees-Ininlltes-secondsL.____ JSTO Storc value in R n (n = 1, 2, . . . , 9)

[ ~ ~ ~ : J Convert from degrees-min utes-seconds

382738

R C Recall stored value from R n (n= 1, 2, .. , 9). 23, 27, 34,40i ~ ; o l Percent differenceL.__ .JI I x percent of y .r - - ,L ~ E ~ J Degrees mode

Copy x into Y .r - - ,L':'.:'J Radians mode

CHS Change signr - - ,

L ' : : ~ J Grads modeEEX Enter exponentr----'

L ~ ~ E . : ' ~ J Clear stack and R , -R , .

r - - - - 'I em/in IL____ -I

Clear X .SubtractAddMultiplyDivideCentimeters/ inches conversion

[ ~ ~ 2 ~ J Kilograms/pounds conversionr - - - - '

L ~ t ~ ~ ~ J Liters/gallons conversioni ~ A - s ~ ~ l Recall last x argument .L____ J

[ ~ ~ J Pi constant (3.14 . . . . ) .i ~ ~ l Decrement sllinmationL__ J

212037

11 , 22, 24, 3437143715

13 , 26, 34, 419, 11, 13

11 ,2 2, 2811 ,22, 27

11 , 12, 22,2 811 , 12, 22, 28

313232

12, 261834, 4034,40Summation@]-0 .8 Numeric key set . . . . . . . . . . . . . . . . . . . . . . . . . 11


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Documents

HP-45 Owner's Handbook 1973 Color